Finite Group DatabasebetaFinite Group Databasebeta| order | 7252 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C4×C7×C9 (order 3024) · Inn(G) = C1 · Out(G) = C22×C3×C4×C7×C9 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C7252 |
| abelian | C4×C37×C49 |
| multiplicative | (ℤ/7253)ˣ, (ℤ/14506)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C2×C7 | C2×C7×C37 |
| socle | C2×C7×C37 | C2×C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
18 conjugacy classes of subgroups.
7252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7252, 1);